Solve the two pairs of simultaneous equations:

\begin{matrix} x + 0.99999 y & = & 2.99999 \\ 0.99999 x + y & = & 2.99998 \end{matrix}

and

\begin{matrix} x + 1.00001 y & = & 2.99999 \\ 0.99999 x + y & = & 2.99998 . \end{matrix}

Explain why the solutions are so different and yet the pairs of equations are nearly identical.

NOTES AND BACKGROUND
In this question a small perturbation in one of a pair of equations makes a big change in the solutions. Considering the geometrical properties of the lines represented by the equations helps to de-mystify the results.